Kelly Criterion Calculator: Find Your Optimal Bet Size

A Kelly Criterion calculator turns three inputs, the odds, your estimate of the win chance, and your bankroll, into the stake the Kelly model treats as the fastest way to grow a bankroll over the long run. It is the standard answer to the hardest question in betting, which is not what to bet but how much. The calculator below sizes any bet in one step, and it adds the part most Kelly calculators leave out: what that stake actually does to your growth once your win probability estimate is slightly wrong. Kelly is best read as a ceiling rather than a target.

Try It: Kelly Criterion Calculator

Enter a price and your estimated win chance, then watch two numbers. Your stake is the Kelly answer. Share of the growth on offer is how much of the achievable compounding that stake actually captures once the overshoot slider says your estimate was a little optimistic. Switch the stake size from Full Kelly to Half Kelly and watch it climb.

This runs on getKellyFraction, the same function behind the Kelly Calculator and the stake SmartStake shows next to a positive expected value bet. The rest of this guide explains where the number comes from and why the default reads the way it does.

The Kelly Formula

The Kelly Criterion is usually written like this, where b is the decimal odds minus 1 (your payout per unit staked), p is your estimated chance of winning, and q is 1 minus p:

$f^* = \frac{bp - q}{b}$

That form hides what is really going on. Multiply it out and the numerator collapses into something you already track:

$f^* = \frac{po - 1}{o - 1}$

The top of that fraction, po minus 1, is the expected value of a 1 unit bet. It is your edge. So the whole formula reduces to one sentence:

The Kelly stake is your edge divided by your payout multiple. Nothing more.

Two consequences fall straight out of that. Your stake scales in direct proportion to your edge, so a 5% edge gets exactly half the stake of a 10% edge at the same price. And your stake shrinks as the price lengthens, because a longer price means a bigger b on the bottom, which is why Kelly stakes far less on a +400 shot than a bettor's instinct usually wants to.

A Worked Example

Take a price of +110, decimal 2.10, and suppose you have devigged the sharp market and estimate the true win chance at 52%.

edge  = 0.52 × 2.10 − 1 = 0.092  (9.2%)
b     = 2.10 − 1        = 1.10
Kelly = 0.092 / 1.10    = 0.0836 (8.36% of bankroll)

On a 2,000 dollar bankroll that is a 167 dollar bet. Which is a lot. A bettor who normally risks 1% of a bankroll is being told to risk more than eight times that on a single game, on the strength of a 2 point disagreement with the market.

That reaction is correct, and the reason it is correct is the most useful thing on this page.

Where the Win Probability Comes From

Kelly does not know anything about the game. It takes your number and does arithmetic with it. Feed it a bad probability and it returns a confidently wrong stake, which is why every serious Kelly workflow spends far more effort on the input than the formula.

There are three honest ways to get that number:

• Devig a sharp market. Strip the margin out of a market making book's price and you are left with the market's own estimate of the true chance. That is what the devigging calculator does, and the devigging guide covers the methods and their trade offs. What that number means, and why it is never a price you would bet at, is the subject of no vig fair odds.
• Build a model. A power rating, a regression, or a simulation that outputs a probability for the market you bet. How to build a sports betting model walks the six steps.
• Take a positive expected value tool's number. SmartStake's positive EV engine devigs a sharp reference and compares it to every book, so the win chance arrives already calculated.

One rule holds across all three. If your probability comes from the same book you are betting into, you have no edge, only its margin read back to you.

Why the Kelly Answer Looks Too Big

An 8.36% stake is not a rounding error on a bankroll. Run 200 bets at that size and drawdowns of 30% or more are ordinary, not unlucky. Full Kelly is a growth maximizer, and it buys that growth with variance it makes no attempt to limit.

There is a cleaner way to say it. Full Kelly is the stake that maximizes growth on the assumption that your probability is exactly right. Every other property people attribute to it, safety, ruin avoidance, discipline, follows only if that assumption holds.

It never holds. So the question is not whether to shade the Kelly number down. It is how much, and what it costs you.

The Growth Curve Behind the Formula

Kelly maximizes the average logarithm of your bankroll, which is the compounding rate. For a single bet at decimal odds o with true win chance p, staking a fraction f of the bankroll, that rate is:

$G(f) = p \ln(1 + (o-1)f) + (1-p)\ln(1-f)$

Plot that and you get a hill. It rises from zero, peaks exactly at the Kelly fraction, and falls away on the other side. Two features of the hill matter more than the peak itself:

• It is nearly flat near the top. Stake half the optimal amount and you keep roughly 75% of the growth, for half the risk. Underbetting is cheap.
• It crosses back through zero at twice the optimal stake. Bet double Kelly and the expected compounding rate is zero, so a real edge grows nothing at all. Past that, the model implies steady losses despite the edge being genuine.

That asymmetry is the whole argument. The penalty for staking too little is a shallow slope. The penalty for staking too much is a cliff. And since nobody knows their true edge, you cannot be sure which side of the peak you are standing on.

What One Wrong Point Costs

Here is where the ceiling framing earns itself. Go back to the worked example, but suppose your 52% estimate was 2 points optimistic and the true chance is 50%. The price is unchanged.

Your real edge was never 9.2%. At 50% and decimal 2.10, it is 5%. So the true Kelly stake is 4.55% of the bankroll, and the 8.36% you calculated is 1.84 times the correct size. Because Kelly is edge divided by b, a proportional error in the edge is a proportional error in the stake, one for one.

This is what that does to the illustrative growth, at the true 50% win chance:

Read the middle two rows again. Half Kelly on a flawed estimate captures almost all of the available growth. Full Kelly on the same flawed estimate captures under a third of it. Halving your stake did not cost you growth here. It bought you growth back, because it corrected an error you did not know you had made.

That is a general result, not a quirk of these numbers. Any bettor who systematically overstates edge by a couple of points is playing at close to double Kelly while believing they are playing at full Kelly, and double Kelly is the line where growth disappears entirely.

Drag the overshoot slider in the calculator above to 0 and Full Kelly reclaims the top spot, exactly as the theory says. It is right, on the one input nobody has.

Fractional Kelly in Practice

A quarter to a half of full Kelly is the working range for most bettors, and the choice inside that range is a real one:

• Half Kelly if your probabilities come from devigged sharp markets and you have a record long enough to show they hold up. You stay close to the model's peak growth with materially smaller swings.
• Quarter Kelly if you are betting your own model, betting new markets, or you simply want the smoother ride. You give up growth in exchange for drawdowns roughly a quarter the size.
• Never above full Kelly. There is no version of the maths where that is the better bet.

A useful discipline on top of the fraction: cap any single stake at a fixed share of the bankroll, say 2% or 3%, no matter what the formula says. That cap is doing the same job the fraction does, which is protecting you from your own probability estimates, but it also catches the case where a fat priced longshot produces an unusually large Kelly number. Bankroll management covers how the cap fits alongside flat and percentage staking.

Kelly When Bets Overlap

The formula assumes one bet at a time. Each stake is a fraction of a bankroll that has already settled the previous result, and that sequencing is what makes the compounding argument work.

A Saturday slate breaks it. Ten bets running at once are ten fractions of the same untouched bankroll, so the exposure adds up in a way the formula never modelled. Correlated bets break it harder, because bets that can lose together behave like one much larger bet.

The practical fix is not complicated. Size each bet as usual, then scale the whole group down so total exposure at any one moment stays near what a single Kelly stake would have risked. Same discipline as the fraction, applied across the slate rather than the bet.

Kelly Inside SmartStake

Kelly stakes are not a separate exercise from finding the bet. In the positive EV tool, each bet arrives with a devigged true probability already attached, and the recommended stake is that probability run through the same Kelly function this page's calculator uses. The stake and the edge come from one number, calculated once.

Two habits keep that number honest. Shop the price first, because a better number is a bigger edge and therefore a bigger justified stake, which line shopping covers. And track your closing line value afterwards, because it is the fastest evidence available on whether your probability estimates were ever right. If your bets are not beating the closing line, the problem is the input, and no staking formula fixes a bad input.

Frequently Asked Questions

What is the Kelly Criterion in betting?

The Kelly Criterion is a formula that returns the fraction of your bankroll to stake on a bet, given the odds and your estimate of how often the bet wins. It is the stake that maximizes the long run compounding rate of the bankroll: bet less and you grow slower, bet more and you grow slower again while carrying far more risk. It needs a genuine edge to return anything at all, and returns zero when the price matches your estimated win chance.

How do you calculate the Kelly bet size?

The Kelly stake is the edge divided by the payout multiple on the bet. In the standard form, f equals (bp minus q) divided by b, where b is the decimal odds minus 1, p is your estimated win chance and q is 1 minus p. At decimal 2.10 with a 52% estimate, the edge is 9.2% and b is 1.10, so the Kelly stake is 8.36% of the bankroll. A calculator does this instantly, but the arithmetic is one line.

Should you bet full Kelly or fractional Kelly?

Most disciplined bettors stake a quarter to a half of full Kelly. Fractional Kelly is not simply the cautious choice, it is often the better one, because full Kelly is only optimal if your win probability is exactly right and it never is. In the illustrative example on this page, a win chance overstated by 2 points leaves half Kelly capturing almost all of the available growth while full Kelly captures under a third of it.

What happens if you bet more than the Kelly Criterion says?

Growth falls away much faster above the Kelly stake than below it. Bet double the Kelly fraction and the expected compounding rate drops to zero, so a genuine edge stops growing the bankroll at all. Past that point the model implies losing money on average despite betting into a real edge, which is why overstating your edge is more damaging than understating it.

Does the Kelly Criterion work for parlays or several bets at once?

The formula assumes bets settle one after another, so each stake is a fraction of a bankroll that has already absorbed the last result. Bets that run at the same time break that assumption, and correlated bets break it hardest, because they can all lose together. The practical fix is to size each bet as normal and then scale the whole group down so the total exposure at any one moment stays within what a single Kelly stake would have risked.

Size Your Next Bet

The Kelly Criterion answers how much, but only as well as you answer how likely. Get the probability from a devigged sharp market, run it through the formula, then stake a fraction of what it tells you, because the cost of overestimating your edge is far steeper than the cost of underestimating it.

Run your next price through the Kelly Calculator, or let SmartStake's positive EV tool devig the market and size the bet in one step.